Invariant Neutral Subspaces for Symmetric and Skew Real Matrix Pairs
Peter Lancaster, Leiba Rodman · Canadian Journal of Mathematics · 1994
Abstract Real matrix pairs ( A,H ) satisfying det H ≠ 0, H T = ε H , and HA - η A T H , where ε, η take the values +1 or —1, are considered. It is shown that maximal A -invariant H -neutral subspaces have the same dimension (depending on ε and η), called the order of neutrality of the pair ( A, H ). The order of neutrality of definitizable pairs is investigated. In particular, this concept is used to obtain lower bounds for the number of pure imaginary eigenvalues of low rank perturbations of definitizable pairs when (ε,η) = (1, - 1 ) and when (ε,η) = (—1,—1).